Physiological parameters can be extracted by using a pharmacokinetic model to analyze dynamic contrast enhanced (DCE) MRI data. However, this requires accurate measurements of the arterial input function (AIF) (1). The AIF is often measured from a major artery under the assumption that this represents the true input of contrast media to the tissue, but these measurements are subject to large errors due to T2* effects and water exchange (2). Thus, population AIFs are often employed in pharmacokinetic modelling. The mathematical form of the population AIF can be as simple as double exponential functions with four parameters (3) or as complicated as double Gaussian functions with 10 parameters (4). Obviously, the simple exponential AIFs cannot accurately model the 1^st and 2^nd passes of contrast agent circulations. Conversely, the complicated mathematical AIF can accurately model both passes, but may be hard to use with noisy and/or low temporal resolution data. Therefore, it’s desirable to have the mathematical AIF that can accurately model both passes with the lowest possible number of parameters. Here, we present a new mathematical form for AIF with 8-parameter, verified with AIFs measured from the femoral artery following injection of 1/7 of the standard dose of contrast agent.

The study was compliant with the HIPAA and approved by our IRB, and all participants provided written informed consent. Twenty-three patients with biopsy confirmed prostate cancer were enrolled in this study (mean age=57.3 years, range 43 to 70 years). Images were acquired with a Philips Achieva 3T TX scanner using the combination of a phased array and endorectal coil. After other clinically required scans, axial T1-weighted DCE-MRI data (TR/TE=4.2/1.5 ms, FOV=180×372 mm², number of slices=24, slice thickness=3.5 mm, in plane resolution=1.5×2.8 mm², reconstructed resolution=1.1×1.1 mm², SENSE factor=3.5, partial Fourier factor=0.625, flip angle=10°) were acquired with temporal resolution of 1.5 s and for a total of ~2.25 minutes. The dose of contrast injected was 0.015 mmol/kg. This lower dose was allowed a better estimate of the true AIF, since it is less affected by T2* changes and water exchange.

The AIF (n=23) was measured by manually tracing region of interest (ROI) over cross sections of the external femoral artery on 6-10 slices. The average signal intensity S(t) over ROI was calculated first, then the relative signal enhancement curve (S_r(t)) as function of time (t) was calculated: $$$S_{r}(t)=(S(t)-S_{0})/S_{0}$$$ , where S₀ is the baseline signal. To minimize errors in calculations of contrast media concentration due to heterogeneous B1 fields, the S_r(t) was used to verify our newly developed empirical mathematical model (EMM) AIF:

$$S_{r}(t)=A_{0}(1+\sum_{n=1}^2A_{n}\exp(-(t-t_{n})^{2}/2\sigma_{n}^{2}))\cdot\exp(-\beta\cdot t)$$

where A₀ and A_n are scaling constants, t_n and σ_n are centers and widths of the n^th Gaussian function, and β is the decay constant. The inverse tangent function was used to modulate the Gaussian functions so that S_r(0)=0. This is important because Gaussian function is not equal to zero at t=0. Here we test this model by fitting signal enhancement as a function of time. However, when a standard DCE-MRI protocol is used, conversion from enhancement to concentration does not significantly affect the shape of the AIF (5).

For a typical patient, Figure 1 shows an axial slice post-contrast agent administration DCE-MRI with the femoral artery indicated by red arrow. Figure 2 shows the corresponding directly measured AIF (dots) and the fits obtained with the EMM-AIF (red line). The 1^st and 2^nd pass peaks of the contrast bolus are accurately fitted by our model. The average plus standard deviation for all eight parameters of EMM-AIF over all 23 subjects are given in Table 1. The parameter governing the 2^nd pass width (σ₂) had the largest coefficient of variation. Finally, figure 3 shows the AIF plotted by using the average parameters listed in the Table 1.Our newly developed eight-parameter EMM-AIF accurately fits the AIF measured from patients’ external femoral artery. Although many mathematical forms of AIF have been developed, our model fits both 1^st and 2^nd passes accurately with a relatively small number of parameters. With low SNR or low temporal resolution data, it is hard to fit the curves with more parameters. Therefore, models with fewer parameters are preferable in DCE-MRI data analysis. Importantly, the EMM-AIF equals zero at t=0, in contrast to models using Gaussian functions only (4). This is important because measured contrast media uptake during the first few seconds after injection has a strong influence on K^trans values. The EMM-AIF should be useful for both pre-clinical research and in clinical diagnosis of cancers and treatment evaluation using DCE-MRI.